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We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…
Physics-based simulations typically operate with a combination of complex differentiable equations and many scientific and geometric inputs. Our work involves gathering data from those simulations and seeing how well tree-based machine…
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer…
Physics analysis in astroparticle experiments requires the capability of recognizing new phenomena; in order to establish what is new, it is important to develop tools for automatic classification, able to compare the final result with data…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
We provide a formal definition for a class of algorithms known as "particle methods". Particle methods are used in scientific computing. They include popular simulation methods, such as Discrete Element Methods (DEM), Molecular Dynamics…
General aspects about the thermodynamics of astrophysical systems are discussed, overall, those concerning to astrophysical systems in mutual interaction (or the called \emph{open astrophysical systems}). A special interest is devoted along…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
After the discovery of the gravitational waves and the observation of neutrinos of cosmic origin, we have entered a new and exciting era where cosmic rays, neutrinos, photons and gravitational waves will be used simultaneously to study the…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
In this contribution, I give an overview of the various approaches toward the numerical modelling of turbulence, particularly, in the interstellar medium. The discussion is placed in a physical context, i. e. computational problems are…
Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other.…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…